Finite Group Databasebeta

C2×C4×#14558713 #34047022

order19072
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#14558713

Splittings

FittingC22×C42×C149 ⋊ C2
SylowC149 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D149
commutatorC2×C149C22×C42
FrattiniC23C23×D149
FittingC22×C42×C149C2
socleC24×C149C23
prime radicalC24×D149C22
cosocleC23×C149C24
hypercenterC22×C42D149
hypocenterC149C2×C4×C22⋊C4
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9536

Conjugacy classes & character table

4816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 6841);