Finite Group Databasebeta

C23×C4×C22⋊D7 #14260359

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×C4×C22⋊D7

Splittings

FittingC25×C4×C7 ⋊ C2
SylowC7 ⋊ C23×C4×D4

Subgroups

subgroupG/H
centerC24×C4C2×D7
commutatorC2×C7C25×C4
FrattiniC22C25×D7
FittingC25×C4×C7C2
socleC25×C7C23
prime radicalC24×C22⋊D7C2
cosocleC22×C7C26
hypercenterC25×C4D7
hypocenterC7C23×C4×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C24×C4 ◁ C25×C4

19998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076131);