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C22×D157⋊C8 #23758344

order10048
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D157⋊C8
unambiguous semidirect productD157⋊(C22×C8)

Splittings

derived, SylowC157 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#10597845
commutator, hypocenterC157C23×C8
FrattiniC2C23×#10597845
FittingC22×C4×C157C4
socleC23×C157C2×C4
prime radicalC23×D157C4
cosocleDic157C24
LCSG ▷ C157
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#10597845)⋊C8, #34115797, #34115803, …
maximal normal subgroup ofC2×(C2×#10597845)⋊C8, #34115797, #34115803, …
maximal quotient ofC22×C4×#11929441, C2×C4×D157⋊C8, C2×D157⋊(C22⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1620);