#34319848

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁸

Aliases

No aliases for this group.

Splittings

Fitting	C₇₉×#2846 ⋊ C₂
Sylow	C₇₉ ⋊ #23900

Subgroups

	subgroup	G/H
center	C₂²	C₂×#14579129
commutator, cosocle	C₂⁴×C₇₉	C₂⁴
Frattini	C₂⁴	C₂³×D₇₉
Fitting	C₇₉×#2846	C₂
socle	C₂²×C₇₉	C₂×#120
hypercenter	#2846	D₇₉
hypocenter	C₇₉	#23900
LCS	G ▷ C₂⁴×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ #2846

3520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 1264

A minimal faithful permutation representation — 4 generators on 91 points:

(5,6)(7,9)(8,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90);(2,4)(5,7)(6,9)(8,11)(10,12);(1,2)(3,4)(5,6)(7,9)(8,10)(11,12)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91);(9,12)

Polycyclic presentation:

2^8,79|b^a=be,c^a=cf,d^a=de,c^b=cg,f^b=fh,i^b=i^78,e^c=eh,f^d=fh,i^d=i^78

Conjugacy classes & character table

1762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 201147);