Finite Group Databasebeta

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C22⋊C4×Dic298 #34047526

order19072
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic298

Splittings

SylowC149 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D149
commutatorC22×C149C23×C4
FittingC4×C22⋊C4×C149C2
socle, cosocleC23×C149C24
prime radicalC24×C149C23
hypercenterC4×C22⋊C4D149
hypocenterC149Q8×C22⋊C4
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9536

Conjugacy classes & character table

3010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19072, 7345);