Finite Group Databasebeta

C2×C22⋊C4×C22⋊D7 #13512967

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×C22⋊C4×C22⋊D7

Splittings

FittingC23×C7×C22⋊C4 ⋊ C2
SylowC7 ⋊ C2×D4×C22⋊C4

Subgroups

subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC23×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC24×C22⋊D7C2
cosocleC23×C7C25
hypercenterC23×C22⋊C4D7
hypocenterC7C2×D4×C22⋊C4
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C22⋊C4

8774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 328739);