Finite Group Databasebeta

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C4×#88722 #13152714

order1728
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25×C3

Aliases

direct productC4×#88722

Splittings

FittingC4×Q8×H(3,𝔽3) ⋊ C2
SylowH(3,𝔽3) ⋊ C4×#41

Subgroups

subgroupG/H
centerC2×C4C22×(C3⋊D3)⋊C3
commutatorC2×C32C23×C3×C4
Frattini, socleC22×C3C23×C3×D3
FittingC4×Q8×H(3,𝔽3)C2
prime radicalC2×#88722C2
cosocleC22×C32C24×C3
hypercenterC4×Q8(C3⋊D3)⋊C3
hypocenterC32C3×C4×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

1155 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 288

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 18777);