Finite Group Databasebeta

C23×#6455 #14260355

order1792
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C213×C4

Aliases

direct productC23×#6455

Splittings

FittingC23×C7×C4⋊C4 ⋊ C2
SylowC7 ⋊ C23×#117

Subgroups

subgroupG/H
centerC25C22×D7
commutatorC2×C7C25×C4
FrattiniC22C25×D7
FittingC23×C7×C4⋊C4C2
socleC25×C7C23
prime radicalC25×D7C22
cosocleC22×C7C26
hypercenterC23×C4⋊C4D7
hypocenterC7C23×#117
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C25 ◁ C23×C4⋊C4

14334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076127);