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C11×#672 #11724835

order880
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C11×C16 · Schur multiplier (H2) = C1

Aliases

direct productC11×#672

Splittings

derived, SylowC5 ⋊ C11×C16
HallC5×C11 ⋊ C16

Subgroups

subgroupG/H
center, hypercenterC8×C11D5
commutator, hypocenterC5C11×C16
FrattiniC8D5×C11
FittingC5×C8×C11C2
socle, prime radicalC2×C5×C11C8
cosocleC5×C8C2×C11
LCSG ▷ C5
UCSC1 ◁ C8×C11

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,14)(15,16)(17,18,19,22,20,23,25,28,21,24,26,29,27,30,31,32);(12,13,15,16,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC11×#3928, C11⋊#3928, D11×#672, …
maximal normal subgroup ofC11×#3928, C11⋊#3928, D11×#672, …
maximal quotient ofC11×#3926, C2×C11×#672

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 3);