Finite Group Databasebeta

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C4×#88530 #13143783

order1728
isoclinismisoclinic class of #88528
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×#88530

Splittings

SylowH(3,𝔽3) ⋊ C4×Q16

Subgroups

subgroupG/H
centerC2×C3×C4C4⋊(C3⋊D3)
commutatorC4×H(3,𝔽3)C22×C4
FrattiniC2×C3×C4C22×C3⋊D3
FittingC4×C8×H(3,𝔽3)C2
socleC22×C3C2×C4⋊(C3⋊D3)
prime radicalC22×H(3,𝔽3)C2×D4
cosocleC2×C4×H(3,𝔽3)C23
hypercenterC3×C4×C8C3⋊D3
hypocenterH(3,𝔽3)C4×Q16
LCSG ▷ C4×H(3,𝔽3) ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×C8

605 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 605 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 576

Conjugacy classes & character table

212 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 9846);