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C22×#13095402 #20259997

order6176
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC22×#13095402

Splittings

Fitting, socleC22×C193 ⋊ C8
derived, SylowC193 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22#13095402
commutator, hypocenterC193C22×C8
FrattiniC1G
Fitting, socleC22×C193C8
LCSG ▷ C193
UCSC1 ◁ C22

76 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#13095402)⋊C4, C2×C4×#13095402, C2×C22⋊#13095402, …
maximal normal subgroup of(C2×#13095402)⋊C4, C2×C4×#13095402, C2×C22⋊#13095402, …
maximal quotient ofC2×C4×#13095402, C2×C22⋊#13095402, C2×C4⋊#13095402, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6176, 244);