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C11×Dic20 #11724910

order880
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×Dic20

Splittings

HallC5×C11 ⋊ Q16
SylowC5 ⋊ C11×Q16

Subgroups

subgroupG/H
centerC2×C11D20
commutator, cosocleC4×C5C22×C11
FrattiniC4C2×D5×C11
FittingC5×C8×C11C2
socle, prime radicalC2×C5×C11D4
hypercenterC8×C11D5
hypocenterC5C11×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C11 ◁ C4×C11 ◁ C8×C11

36 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)(12,13,14,15,16,17,18,19)(20,27,26,25,24,23,22,21)(28,29,30,31,32);(12,20,16,24)(13,21,17,25)(14,22,18,26)(15,23,19,27)(29,32)(30,31)

Conjugacy classes & character table

253 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13182269, #13182274, #13182275, …
maximal normal subgroup of#13182269, #13182274, #13182275, …
maximal quotient ofC11×#3950, C11×#3948, C2×C11×Dic20

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(880, 78);