Finite Group Databasebeta

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C22×#14582142 #24925402

order10832
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14582142
unambiguous semidirect productD677⋊(C2×C4)

Splittings

Fitting, socleC22×C677 ⋊ C4
derived, SylowC677 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22#14582142
commutator, hypocenterC677C22×C4
FrattiniC1G
Fitting, socleC22×C677C4
prime radicalC22×D677C2
cosocleD677C23
LCSG ▷ C677
UCSC1 ◁ C22

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

692 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14582142)⋊C4, C2×C4×#14582142, C2×C22⋊#14582142, …
maximal normal subgroup of(C2×#14582142)⋊C4, C2×C4×#14582142, C2×C22⋊#14582142, …
maximal quotient ofC2×C4×#14582142, C2×C22⋊#14582142, C2×C4⋊#14582142, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10832, 51);