C₁₇×(C₂²⋊C₉)⋊C₂ #11927469

order	1224
isoclinism	isoclinic class of (C₂²⋊C₉)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₇×(C₂²⋊C₉)⋊C₂
unambiguous semidirect product	(C₂²⋊C₉)⋊(C₂×C₁₇)

C₂²⋊C₉ ⋊ C₂×C₁₇

	subgroup	G/H
center, hypercenter	C₁₇	(C₂²⋊C₉)⋊C₂
commutator, cosocle, hypocenter	C₂²⋊C₉	C₂×C₁₇
Frattini	C₃	C₁₇×S₄
Fitting, socle	C₂²×C₃×C₁₇	D₃
LCS	G ▷ C₂²⋊C₉
UCS	C₁ ◁ C₁₇

36 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 306

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(23,25)(24,28)(26,27)(29,30);(19,20,21)(22,30,25,28,27,26,24,23,29)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1224, 42);