Finite Group Databasebeta

C22×Dic172 #14583676

order2752
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic172

Splittings

SylowC43 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23D172
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingC22×C8×C43C2
socle, prime radicalC23×C43D4
hypercenterC22×C8D43
hypocenterC43C22×Q16
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2752

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1326);