Finite Group Databasebeta

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C23×Dic373 #26045827

order11936
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC23×Dic373

Splittings

derived, SylowC373 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC24D373
commutator, hypocenterC373C23×C4
FrattiniC2C23×D373
Fitting, socle, prime radicalC24×C373C2
cosocleC2×C373C24
LCSG ▷ C373
UCSC1 ◁ C24

236 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3008 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×#26045699, C22⋊C4×Dic373, #37559280, …
maximal normal subgroup ofC2×#26045699, C22⋊C4×Dic373, #37559280, …
maximal quotient ofC22×C4×Dic373, C22×C22⋊Dic373, C22×C4⋊Dic373, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11936, 181);