Finite Group Databasebeta

← Prev (#21440739) Next (#21440741) →

C22×#14515358 #21440740

order7712
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14515358

Splittings

Fitting, socleC22×C241 ⋊ C8
derived, SylowC241 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#14515358
commutator, hypocenterC241C22×C8
FrattiniC1G
Fitting, socleC22×C241C8
LCSG ▷ C241
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14515358)⋊C4, C2×C4×#14515358, C2×C22⋊#14515358, …
maximal normal subgroup of(C2×#14515358)⋊C4, C2×C4×#14515358, C2×C22⋊#14515358, …
maximal quotient ofC2×C4×#14515358, C2×C22⋊#14515358, C2×C4⋊#14515358, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7712, 244);