#38760313

order	25284
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

derived, Hall	C₇²×C₄₃ ⋊ C₃×C₄
Hall	C₄₃×C₇⋊Dic₇ ⋊ C₃
Hall	#20263479 ⋊ C₄
Hall	C₇⋊Dic₇ ⋊ C₄₃⋊C₃
Sylow	C₇² ⋊ C₄×C₄₃⋊C₃
Sylow	C₄₃ ⋊ #10596874

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	#27162406
commutator, hypocenter	C₇²×C₄₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₄₃	C₂×C₃
prime radical	C₂×#20263479	C₂
LCS	G ▷ C₇²×C₄₃
UCS	C₁ ◁ C₂

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 8428

A minimal faithful permutation representation — 3 generators on 61 points:

(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,33)(18,26,31)(21,29,28)(23,32,25)(27,36,40)(30,37,39)(34,41,35)(38,42,43)(44,45,46,47)(49,52,53,50,51,54)(56,59,60,57,58,61);(1,2,4,8,15,20,5,9,16,25,35,32,12,19,28,24,34,41,22,31,39,36,14,23,33,40,43,42,26,7,13,21,30,38,37,17,3,6,11,18,27,29,10)(55,56,58,61,60,59,57);(48,49,51,54,53,52,50)

Polycyclic presentation:

2,3,7^2,43,2|a^2=f,c^a=c^6,d^a=d^6,c^b=c^2,d^b=d^2,e^b=e^36

Conjugacy classes & character table

756 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25284, 120);