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C4⋊C4×C22⋊#64408 #34014681

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC4⋊C4×C22⋊#64408

Splittings

FittingC22×C4⋊C4×C73 ⋊ C4
SylowC73 ⋊ C22⋊C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
FittingC22×C4⋊C4×C73C4
socleC23×C73C23×C4
prime radicalC24×D73C23
cosocleC23×D73C24
hypercenterC22×C4⋊C4#64408
hypocenterC73C22⋊C4×C4⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1098265);