Finite Group Databasebeta

C22×Q8×D43 #14583722

order2752
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×Q8×D43

Splittings

FittingC22×Q8×C43 ⋊ C2
SylowC43 ⋊ C23×Q8

Subgroups

subgroupG/H
centerC23C22×D43
commutator, cosocleC2×C43C25
FrattiniC2C24×D43
FittingC22×Q8×C43C2
socleC23×C43C23
prime radicalC23×D43C22
hypercenterC22×Q8D43
hypocenterC43C23×Q8
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×Q8

850 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1372);