C₂²×#19127425 #35370190

order	21248
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂²×#19127425

Splittings

Sylow

C₈₃ ⋊ C₂²×#323

Subgroups

	subgroup	G/H
center	C₂⁴	C₂²⋊Dic₈₃
commutator	C₂²×C₈₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₂³×C₂²⋊C₄×C₈₃	C₂
socle	C₂⁴×C₈₃	C₂²⋊C₄
prime radical	C₂⁶×C₈₃	C₄
cosocle	C₂²×C₄×C₈₃	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₈₃
hypocenter	C₈₃	C₂²×#323
LCS	G ▷ C₂²×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×C₂²⋊C₄

2878 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 4 generators on 103 points:

(13,15)(14,17)(16,20)(18,19)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(5,6,7,9,8,10,11,12)(13,14)(15,19,20,17)(16,18)(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)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103);(3,4);(1,2)

Conjugacy classes & character table

3368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 135354);

C22×#19127425 #35370190