Finite Group Databasebeta

C22×#90237 #14260383

order1792
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC22×#90237

Splittings

FittingC22×C4×C7×D4 ⋊ C2
SylowC7 ⋊ C22×#520

Subgroups

subgroupG/H
centerC24C23×D7
commutatorC2×C7C25×C4
FrattiniC22C25×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC23×#1159C2
cosocleC22×C7C26
hypercenterC22×C4×D4D7
hypocenterC7C22×#520
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C22×C4×D4

12270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076155);