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C11×C3⋊Dic21 #14583897

order2772
isoclinismisoclinic class of C3⋊D21
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C3⋊Dic21
unambiguous semidirect productC3⋊(C11×Dic21)
unambiguous semidirect productC7⋊(C11×C3⋊Dic3)

Splittings

derived, HallC32×C7 ⋊ C4×C11
HallC32×C7×C11 ⋊ C4
HallC32×C11 ⋊ Dic7
HallC7×C11 ⋊ C3⋊Dic3
SylowC32 ⋊ C11×Dic7
SylowC7 ⋊ C11×C3⋊Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D21
commutator, hypocenterC32×C7C4×C11
FrattiniC2C11×C3⋊D21
Fitting, socle, prime radicalC2×C32×C7×C11C2
cosocleC2×C32×C7C2×C11
LCSG ▷ C32×C7
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 2772

A minimal faithful permutation representation — 3 generators on 28 points:

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

Conjugacy classes & character table

726 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11⋊C5×C3⋊Dic21, C5×C11×C3⋊Dic21, C11×C3⋊Dic105, …
maximal normal subgroup ofC11⋊C5×C3⋊Dic21, C5×C11×C3⋊Dic21, C7×C11×C3⋊Dic21, …
maximal quotient ofC5×C11×C3⋊Dic21, C11×C3⋊Dic105, C11×C3⋊(C3⋊(C7⋊AGL(1,𝔽5))), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2772, 53);