Finite Group Databasebeta

← Prev (#10597649) Next (#10597651) →

C13×(C2×D3)⋊C4 #10597650

order624
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C22

Aliases

direct productC13×(C2×D3)⋊C4
unambiguous semidirect product(C2×D3)⋊(C4×C13)

Splittings

FittingC2×C3×C4×C13 ⋊ C2
HallC3×C13 ⋊ C22⋊C4
SylowC3 ⋊ C13×C22⋊C4

Subgroups

subgroupG/H
centerC22×C13C2×D3
commutatorC2×C3C2×C4×C13
FrattiniC22C2×D3×C13
FittingC2×C3×C4×C13C2
socleC22×C3×C13C22
prime radicalC22×D3×C13C2
cosocleC22×C3C22×C13
hypercenterC2×C4×C13D3
hypocenterC3C13×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C13 ◁ C2×C4×C13

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 312

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16)(17,18,19,20)(22,24);(15,16)(21,22)(23,24)

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11928432, #11928434, #11928451, …
maximal normal subgroup of#11928432, #11928434, #11928451, …
maximal quotient ofC13×#805, C13×#806, C13×#809, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(624, 87);