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C22×D173⋊C8 #26012562

order11072
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D173⋊C8
unambiguous semidirect productD173⋊(C22×C8)

Splittings

derived, SylowC173 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#10621924
commutator, hypocenterC173C23×C8
FrattiniC2C23×#10621924
FittingC22×C4×C173C4
socleC23×C173C2×C4
prime radicalC23×D173C4
cosocleDic173C24
LCSG ▷ C173
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#10621924)⋊C8, #36369224, #36369230, …
maximal normal subgroup ofC2×(C2×#10621924)⋊C8, #36369224, #36369230, …
maximal quotient ofC22×C4×#13063443, C2×C4×D173⋊C8, C2×D173⋊(C22⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 1620);