Finite Group Databasebeta

C22×#17986719 #32904467

order18176
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#17986719

Splittings

SylowC71 ⋊ C22×#556

Subgroups

subgroupG/H
centerC24C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC22×C4×D4×C71C2
socleC24×C71C24
prime radicalC23×D4×C71C22
hypercenterC22×C4×D4D71
hypocenterC71C22×#556
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4×D4

7846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 1076583);