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Dic11×C52⋊C3 #15693129

order3300
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C5

Aliases

direct productDic11×C52⋊C3
unambiguous semidirect productC11⋊(C4×C52⋊C3)
unambiguous semidirect product(C52×Dic11)⋊C3

Splittings

derived, HallC52×C11 ⋊ C3×C4
HallC52×Dic11 ⋊ C3
HallC11×C52⋊C3 ⋊ C4
SylowC52 ⋊ C3×Dic11
SylowC11 ⋊ C4×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D11×C52⋊C3
commutator, hypocenterC52×C11C3×C4
Fitting, socle, cosocleC2×C52×C11C2×C3
prime radicalC2×C11×C52⋊C3C2
LCSG ▷ C52×C11
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 660

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15)(16,17,19)(18,22,24)(20,25,28)(21,27,30)(23,26,29);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(16,18,23,28,30)(17,22,26,20,21)(19,25,24,27,29)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×Dic11×C52⋊C3, C11⋊(Dic7⋊(C52⋊C3)), Dic11×C7⋊(C52⋊C3), …
maximal normal subgroup ofC7×Dic11×C52⋊C3, C11×Dic11×C52⋊C3
maximal quotient ofC7×Dic11×C52⋊C3, C11⋊(Dic7⋊(C52⋊C3)), Dic11×C7⋊(C52⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 49);