Finite Group Databasebeta

C2×C4×Dic734 #37554651

order23488
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic734

Splittings

SylowC367 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D367
commutatorC2×C367C23×C4
FrattiniC22C23×D367
FittingC2×C42×C367C2
socle, prime radicalC23×C367C23
cosocleC22×C367C24
hypercenterC2×C42D367
hypocenterC367C2×C4×Q8
LCSG ▷ C2×C367 ▷ C367
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23488

Conjugacy classes & character table

5896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 1014);