Q₈×Dic₁₄ #90257

order	448
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

Q₈×Dic₁₄

C₇ ⋊ Q₈²

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₇
commutator, socle, prime radical, cosocle	C₂²×C₇	C₂⁴
Fitting	C₄×C₇×Q₈	C₂
hypercenter	C₄×Q₈	D₇
hypocenter	C₇	Q₈²
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

212 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,4,6,7,5,3)(16,18,19,23)(17,20,21,22);(2,3)(4,5)(6,7)(16,17,19,21)(18,22,23,20);(8,10,11,15)(9,12,13,14);(8,9,11,13)(10,14,15,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1019);