Finite Group Databasebeta

C22×#10621877 #14583659

order2752
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#10621877

Splittings

SylowC43 ⋊ C22×M16

Subgroups

subgroupG/H
centerC22×C4C2×D43
commutatorC2×C43C23×C4
FrattiniC4C23×D43
FittingC23×C4×C43C2
socleC23×C43C2×C4
prime radicalC24×C43C4
cosocleC4×C43C24
hypercenterC23×C4D43
hypocenterC43C22×M16
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1309);