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C4⋊C4×Dic244 #29698446

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic244

Splittings

SylowC61 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC8×C4⋊C4×C61C2
socle, prime radicalC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC8×C4⋊C4D61
hypocenterC61C4⋊C4×Q16
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15616

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 188001);