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C11×#5997 #14524167

order2156
isoclinismisoclinic class of #5997
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×#5997

Splittings

Fitting, socle, HallC72×C11 ⋊ C4
derived, SylowC72 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC11#5997
commutator, hypocenterC72C4×C11
FrattiniC1G
Fitting, socleC72×C11C4
prime radicalC11×C7⋊D7C2
cosocleC7⋊D7C2×C11
LCSG ▷ C72
UCSC1 ◁ C11

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 25
transitive degreeμt(G) = 154

A minimal faithful permutation representation — 2 generators on 25 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×#13183676, C121×#5997, C112×#5997, …
maximal normal subgroup ofC121×#5997, C112×#5997, C11×C13×#5997, …
maximal quotient ofC11×#13183676, C121×#5997, C112×#5997, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2156, 22);