Finite Group Databasebeta

C2×C42×D373 #37559866

order23872
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C42×D373

Splittings

FittingC2×C42×C373 ⋊ C2
derived, SylowC373 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC2×C42D373
commutator, hypocenterC373C22×C42
FrattiniC22C23×D373
FittingC2×C42×C373C2
socleC23×C373C23
prime radicalC23×D373C22
cosocleC22×C373C24
LCSG ▷ C373
UCSC1 ◁ C2×C42

498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11936

Conjugacy classes & character table

6016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23872, 993);