Finite Group Databasebeta

C2×Q8×Dic523 #45690671

order33472
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic523

Splittings

SylowC523 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D523
commutatorC2×C523C23×C4
FrattiniC22C23×D523
FittingC22×Q8×C523C2
socle, prime radicalC23×C523C23
cosocleC22×C523C24
hypercenterC22×Q8D523
hypocenterC523C2×C4×Q8
LCSG ▷ C2×C523 ▷ C523
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33472

Conjugacy classes & character table

5260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33472, 1015);