Finite Group Databasebeta

C22×#89505 #14220125

order1792
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#89505

Splittings

FittingC22×C7×C22⋊C8 ⋊ C2
SylowC7 ⋊ C22×#452

Subgroups

subgroupG/H
centerC24C2×D28
commutator, cosocleC2×C4×C7C25
FrattiniC2×C4C24×D7
FittingC22×C7×C22⋊C8C2
socleC24×C7C2×D4
prime radicalC23×#1157C2
hypercenterC22×C22⋊C8D7
hypocenterC7C22×#452
LCSG ▷ C2×C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

5110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1035897);