Finite Group Databasebeta

C2×C22⋊C8×D149 #34053121

order19072
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D149

Splittings

FittingC2×C22⋊C8×C149 ⋊ C2
SylowC149 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D149
commutatorC2×C149C23×C8
FrattiniC2×C4C23×D149
FittingC2×C22⋊C8×C149C2
socleC23×C149C22×C4
prime radicalC24×D149C4
cosocleC2×C4×C149C24
hypercenterC2×C22⋊C8D149
hypocenterC149C22×C22⋊C8
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4768

Conjugacy classes & character table

3040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 12940);