Finite Group Databasebeta

C2×Q8×Dic491 #44537191

order31424
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic491

Splittings

SylowC491 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D491
commutatorC2×C491C23×C4
FrattiniC22C23×D491
FittingC22×Q8×C491C2
socle, prime radicalC23×C491C23
cosocleC22×C491C24
hypercenterC22×Q8D491
hypocenterC491C2×C4×Q8
LCSG ▷ C2×C491 ▷ C491
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31424

Conjugacy classes & character table

4940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 1015);