Finite Group Databasebeta

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C4×#18011896 #34047217

order19072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#18011896

Splittings

FittingC4×C4⋊C4×C149 ⋊ C2
SylowC149 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D149
commutatorC22×C149C23×C4
FrattiniC23C23×D149
FittingC4×C4⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC22×D596C22
hypercenterC4×C4⋊C4D149
hypocenterC149C4×#123
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9536

Conjugacy classes & character table

3016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 7036);