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C3×C52×Dic11 #15693134

order3300
isoclinismisoclinic class of D11
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×Dic11

Splittings

derived, SylowC11 ⋊ C3×C4×C52
HallC3×C52×C11 ⋊ C4
HallC52×C11 ⋊ C3×C4
HallC3×C11 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D11
commutator, hypocenterC11C3×C4×C52
FrattiniC2C3×C52×D11
Fitting, socle, prime radicalC2×C3×C52×C11C2
cosocleC2×C11C2×C3×C52
LCSG ▷ C11
UCSC1 ◁ C2×C3×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 3300

A minimal faithful permutation representation — 2 generators on 28 points:

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

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC52×C11⋊(ΓL(1,𝔽8)⋊C4), C52×ΓL(1,𝔽8)×Dic11, C3×C52×Dic77, …
maximal normal subgroup ofC3×C52×C7×Dic11, C3×C52×C11×Dic11
maximal quotient ofC52×C11⋊(ΓL(1,𝔽8)⋊C4), C52×ΓL(1,𝔽8)×Dic11, C3×C52×Dic77, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 54);