Finite Group Databasebeta

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C2×C4⋊C4×C22⋊D73 #33245268

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4⋊C4×C22⋊D73

Splittings

FittingC23×C4⋊C4×C73 ⋊ C2
SylowC73 ⋊ C2×D4×C4⋊C4

Subgroups

subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC23×C4⋊C4×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC23×C4⋊C4D73
hypocenterC73C2×D4×C4⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C4⋊C4

4718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 328852);