Finite Group Databasebeta

C2×C4×Dic998 #44543563

order31936
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic998

Splittings

SylowC499 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D499
commutatorC2×C499C23×C4
FrattiniC22C23×D499
FittingC2×C42×C499C2
socle, prime radicalC23×C499C23
cosocleC22×C499C24
hypercenterC2×C42D499
hypocenterC499C2×C4×Q8
LCSG ▷ C2×C499 ▷ C499
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31936

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31936, 1014);