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C4⋊C4×Dic284 #32015885

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic284

Splittings

SylowC71 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D284
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC8×C4⋊C4×C71C2
socle, prime radicalC23×C71C22×D4
cosocleC22×C4×C71C24
hypercenterC8×C4⋊C4D71
hypocenterC71C4⋊C4×Q16
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18176

Conjugacy classes & character table

2870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 188001);