Finite Group Databasebeta

C2×#20238593 #26045796

order11936
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#20238593

Splittings

FittingC2×C8×C373 ⋊ C2
SylowC373 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D373
commutatorC2×C373C22×C4
FrattiniC4C22×D373
FittingC2×C8×C373C2
socleC22×C373C2×C4
prime radicalC22×D373C4
cosocleC4×C373C23
hypercenterC2×C8D373
hypocenterC373C2×M16
LCSG ▷ C2×C373 ▷ C373
UCSC1 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2996 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#37559203, C4×#20238593, #37559374, …
maximal normal subgroup of#37559203, C4×#20238593, #37559374, …
maximal quotient ofC2×#26045702, C4×#20238593, C2×#26045704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 150);