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C3×C7×#1039 #14523581

order2100
isoclinismisoclinic class of C5⋊D5
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×#1039

Splittings

derived, SylowC52 ⋊ C3×C4×C7
HallC3×C52×C7 ⋊ C4
HallC52×C7 ⋊ C3×C4
HallC3×C52 ⋊ C4×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C5⋊D5
commutator, hypocenterC52C3×C4×C7
FrattiniC2C3×C7×C5⋊D5
Fitting, socle, prime radicalC2×C3×C52×C7C2
cosocleC2×C52C2×C3×C7
LCSG ▷ C52
UCSC1 ◁ C2×C3×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 2100

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C49×#1039, C7×ΓL(1,𝔽8)⋊#1039, C7×ΓL(1,𝔽8)×#1039, …
maximal normal subgroup ofC3×C49×#1039, C3×C72×#1039, C3×C7×C11×#1039, …
maximal quotient ofC3×C49×#1039, C7×ΓL(1,𝔽8)⋊#1039, C7×ΓL(1,𝔽8)×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 61);