Finite Group Databasebeta

C4×Dic1468 #37554282

order23488
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic1468

Splittings

SylowC367 ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C4D1468
commutatorC4×C367C22×C4
FrattiniC2×C4C22×D367
FittingC4×C8×C367C2
socle, prime radicalC22×C367C2×D4
cosocleC2×C4×C367C23
hypercenterC4×C8D367
hypocenterC367C4×Q16
LCSG ▷ C4×C367 ▷ C2×C367 ▷ C367
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23488

Conjugacy classes & character table

5884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23488, 645);