Finite Group Databasebeta

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C4×#18011871 #34047035

order19072
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#18011871

Splittings

FittingC4×C22⋊C4×C149 ⋊ C2
SylowC149 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D149
commutatorC2×C149C22×C42
FrattiniC23C23×D149
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC22×C22⋊D149C22
hypercenterC4×C22⋊C4D149
hypocenterC149C42×D4
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9536

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, 6854);