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C11×#3866 #13108649

order1628
isoclinismisoclinic class of #3866
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#3866

Splittings

Fitting, socle, HallC11×C37 ⋊ C4
derived, SylowC37 ⋊ C4×C11

Subgroups

subgroupG/H
center, hypercenterC11#3866
commutator, hypocenterC37C4×C11
FrattiniC1G
Fitting, socleC11×C37C4
prime radicalC11×D37C2
cosocleD37C2×C11
LCSG ▷ C37
UCSC1 ◁ C11

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 48
transitive degreeμt(G) = 407

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14,15,17)(16,19,20,26)(18,23,24,22)(21,28,29,37)(25,32,30,33)(27,34,35,31)(36,41,42,40)(38,43,44,39)(45,47,48,46);(12,13,16,21,30,24,17,22,31,39,42,35,26,33,40,46,48,44,37,28,38,45,47,41,32,19,27,36,43,34,23,14,18,25,29,20,15)

Conjugacy classes & character table

143 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11×#3866, C11×C7⋊#3866, C11×#13050652, …
maximal normal subgroup ofC7×C11×#3866, C121×#3866, C112×#3866, …
maximal quotient ofC7×C11×#3866, C11×C7⋊#3866, C11×#13050652, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1628, 5);