Finite Group Databasebeta

C2×#15690754 #20261159

order6208
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#15690754

Splittings

SylowC97 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#13095496
commutatorC8×C97C23
FrattiniC8C22×D97
FittingC2×D8×C97C2
socleC22×C97D8
hypercenterC2×D8D97
hypocenterC97C2×SD32
LCSG ▷ C8×C97 ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

694 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#15690754, #27143591, #27143597, …
maximal normal subgroup ofC4×#15690754, #27143591, #27143597, …
maximal quotient ofC2×#20260536, C2×#20260538, C2×#20260562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 973);