Finite Group Databasebeta

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C22⋊C4×Dic454 #44402569

order29056
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22⋊C4×Dic454

Splittings

SylowC227 ⋊ Q8×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D227
commutatorC22×C227C23×C4
FittingC4×C22⋊C4×C227C2
socle, cosocleC23×C227C24
prime radicalC24×C227C23
hypercenterC4×C22⋊C4D227
hypocenterC227Q8×C22⋊C4
LCSG ▷ C22×C227 ▷ C227
UCSC1 ◁ C23 ◁ C4×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14528

Conjugacy classes & character table

4570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29056, 7345);