Finite Group Databasebeta

C2×Q8×Dic41 #14580802

order2624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×Dic41

Splittings

SylowC41 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC23C22×D41
commutatorC2×C41C23×C4
FrattiniC22C23×D41
FittingC22×Q8×C41C2
socle, prime radicalC23×C41C23
cosocleC22×C41C24
hypercenterC22×Q8D41
hypocenterC41C2×C4×Q8
LCSG ▷ C2×C41 ▷ C41
UCSC1 ◁ C23 ◁ C22×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2624

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 1015);