Finite Group Databasebeta

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C22×C4×#10597845 #23758333

order10048
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#10597845
unambiguous semidirect productD157⋊(C2×C42)

Splittings

FittingC22×C4×C157 ⋊ C4
derived, SylowC157 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#10597845
commutator, hypocenterC157C22×C42
FrattiniC2C23×#10597845
FittingC22×C4×C157C4
socleC23×C157C2×C4
prime radicalC23×D157C22
cosocleC2×D157C24
LCSG ▷ C157
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#10597845, C4×(C2×#10597845)⋊C4, #34115311, …
maximal normal subgroup of#95×#10597845, C4×(C2×#10597845)⋊C4, #34115311, …
maximal quotient ofC2×C42×#10597845, C22×(C2×#10597845)⋊C4, C2×#23758209, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1609);