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C4⋊C4×Dic12 #10813620

order768
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4⋊C4×Dic12

Splittings

SylowC3 ⋊ C4⋊C4×Q16

Subgroups

subgroupG/H
centerC23C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×C8×C4⋊C4C2
socle, prime radicalC23×C3C22×D4
cosocleC22×C3×C4C24
hypercenterC8×C4⋊C4D3
hypocenterC3C4⋊C4×Q16
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ C8×C4⋊C4

926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 768

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 188001);