Finite Group Databasebeta

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C7×Dic3×C25 #14523529

order2100
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic3×C25
unambiguous semidirect productC3⋊(C4×C7×C25)

Splittings

derived, SylowC3 ⋊ C4×C7×C25
HallC3×C7×C25 ⋊ C4
HallC3×C25 ⋊ C4×C7
HallC3×C7 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C7×C25D3
commutator, hypocenterC3C4×C7×C25
FrattiniC2×C5C5×D3×C7
FittingC2×C3×C7×C25C2
socle, prime radicalC2×C3×C5×C7C2×C5
cosocleC2×C3×C5C2×C5×C7
LCSG ▷ C3
UCSC1 ◁ C2×C7×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);(8,10,9,11)(13,14)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofDic3×C25×C49, C72×Dic3×C25, C7×C25×Dic21, …
maximal normal subgroup ofDic3×C25×C49, C72×Dic3×C25, C7×C11×Dic3×C25, …
maximal quotient ofDic3×C25×C49, C72×Dic3×C25, C7×C25×Dic21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 9);