Finite Group Databasebeta

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C23×C4⋊C4×D73 #33992537

order18688
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C215

Aliases

direct productC23×C4⋊C4×D73

Splittings

FittingC23×C4⋊C4×C73 ⋊ C2
SylowC73 ⋊ C24×C4⋊C4

Subgroups

subgroupG/H
centerC25C22×D73
commutatorC2×C73C25×C4
FrattiniC22C25×D73
FittingC23×C4⋊C4×C73C2
socleC25×C73C23
prime radicalC25×D73C22
cosocleC22×C73C26
hypercenterC23×C4⋊C4D73
hypocenterC73C24×C4⋊C4
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C25 ◁ C23×C4⋊C4

19742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

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(18688, 1076121);