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C3×C25×Dic7 #14523526

order2100
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C25×Dic7

Splittings

derived, SylowC7 ⋊ C3×C4×C25
HallC3×C7×C25 ⋊ C4
HallC7×C25 ⋊ C3×C4
HallC3×C7 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25D7
commutator, hypocenterC7C3×C4×C25
FrattiniC2×C5C3×C5×D7
FittingC2×C3×C7×C25C2
socle, prime radicalC2×C3×C5×C7C2×C5
cosocleC2×C5×C7C2×C3×C5
LCSG ▷ C7
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 2100

A minimal faithful permutation representation — 2 generators on 39 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30)(31,32)(33,34,35,36,37,38,39);(29,31,30,32)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC3×C25×Dic49, C25×ΓL(1,𝔽8)⋊Dic7, ΓL(1,𝔽8)×C25×Dic7, …
maximal normal subgroup ofC3×C7×C25×Dic7, C3×C11×C25×Dic7, C3×C13×C25×Dic7, …
maximal quotient ofC3×C25×Dic49, C25×ΓL(1,𝔽8)⋊Dic7, ΓL(1,𝔽8)×C25×Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 6);