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C3×C52×Dic7 #14523578

order2100
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×Dic7

Splittings

derived, SylowC7 ⋊ C3×C4×C52
HallC3×C52×C7 ⋊ C4
HallC52×C7 ⋊ C3×C4
HallC3×C7 ⋊ C4×C52

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52D7
commutator, hypocenterC7C3×C4×C52
FrattiniC2C3×C52×D7
Fitting, socle, prime radicalC2×C3×C52×C7C2
cosocleC2×C7C2×C3×C52
LCSG ▷ C7
UCSC1 ◁ C2×C3×C52

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 24 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C52×Dic49, C52×ΓL(1,𝔽8)⋊Dic7, C52×ΓL(1,𝔽8)×Dic7, …
maximal normal subgroup ofC3×C52×C7×Dic7, C3×C52×C11×Dic7, C3×C52×C13×Dic7, …
maximal quotient ofC3×C52×Dic49, C52×ΓL(1,𝔽8)⋊Dic7, C52×ΓL(1,𝔽8)×Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 58);