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C4×C22⋊D307 #23754221

order9824
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC4×C22⋊D307

Splittings

FittingC22×C4×C307 ⋊ C2
SylowC307 ⋊ C4×D4

Subgroups

subgroupG/H
centerC2×C4C2×D307
commutatorC2×C307C22×C4
FrattiniC22C22×D307
FittingC22×C4×C307C2
socle, cosocleC22×C307C23
prime radicalC2×C22⋊D307C2
hypercenterC22×C4D307
hypocenterC307C4×D4
LCSG ▷ C2×C307 ▷ C307
UCSC1 ◁ C2×C4 ◁ C22×C4

94 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2468 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of(C22⋊D307)⋊C8, C8×C22⋊D307, #34087955, …
maximal normal subgroup of(C22⋊D307)⋊C8, C8×C22⋊D307, #34087955, …
maximal quotient ofC4×C22⋊Dic307, C4×(C2×D307)⋊C4, C4×Dic307⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9824, 107);