Finite Group Databasebeta

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C22×#14578818 #23756595

order10016
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14578818

Splittings

Fitting, socleC22×C313 ⋊ C8
derived, SylowC313 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#14578818
commutator, hypocenterC313C22×C8
FrattiniC1G
Fitting, socleC22×C313C8
prime radicalC22×D313C4
cosocle#11929411C23
LCSG ▷ C313
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

188 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14578818)⋊C4, C2×C4×#14578818, C2×C22⋊#14578818, …
maximal normal subgroup of(C2×#14578818)⋊C4, C2×C4×#14578818, C2×C22⋊#14578818, …
maximal quotient ofC2×C4×#14578818, C2×C22⋊#14578818, C2×C4⋊#14578818, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10016, 244);