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C22×D31⋊C3 #10625253

order744
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C23

Aliases

direct productC22×D31⋊C3
unambiguous semidirect productD31⋊(C22×C3)
unambiguous semidirect product(C31⋊C3)⋊C23
unambiguous semidirect product(C2×C31⋊C3)⋊C22

Splittings

Fitting, socleC22×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C23×C3
HallC22×D31 ⋊ C3
HallC31⋊C3 ⋊ C23

Subgroups

subgroupG/H
center, hypercenterC22D31⋊C3
commutator, cosocle, hypocenterC31C23×C3
FrattiniC1G
Fitting, socleC22×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C22

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 124

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×D31⋊C3)⋊C4, C2×C4×D31⋊C3, C2×C4⋊(D31⋊C3), …
maximal normal subgroup of(C2×D31⋊C3)⋊C4, C2×C4×D31⋊C3, C2×C4⋊(D31⋊C3), …
maximal quotient ofC2×(C31⋊C3)⋊Q8, C2×C4×D31⋊C3, C2×C4⋊(D31⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(744, 44);