Finite Group Databasebeta

C2×D7×#387 #13512111

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×D7×#387

Splittings

FittingC2×C7×#387 ⋊ C2
SylowC7 ⋊ C22×#387

Subgroups

subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#387C2
socleC24×C7C24
prime radicalC24×D7C23
cosocleC23×C7C25
hypercenterC2×#387D7
hypocenterC7C22×#387
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#387

4286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327883);