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C₂×C₇⋊#95 #89980

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

direct product	C₂×C₇⋊#95
unambiguous semidirect product	(C₂×C₇)⋊#95

Splittings

C₇ ⋊ C₂×#95

Subgroups

	subgroup	G/H
center	C₂⁴	C₂×D₇
commutator	C₂×C₇	C₂×C₄²
Frattini	C₂³	C₂²×D₇
Fitting	C₂³×C₄×C₇	C₂
socle, prime radical	C₂⁴×C₇	C₂²
cosocle	C₂³×C₇	C₂³
hypercenter	C₂³×C₄	D₇
hypocenter	C₇	C₂×#95
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11725430, #11725480, #11725481, …
maximal normal subgroup of	#11725430, #11725480, #11725481, …
maximal quotient of	C₂×#89318, C₂×#89319, #11729281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 742);