Finite Group Databasebeta

← Prev (#14523586) Next (#14523588) →

C7×C3⋊#1039 #14523587

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

Aliases

direct productC7×C3⋊#1039
unambiguous semidirect productC3⋊(C7×#1039)

Splittings

derived, HallC3×C52 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4
HallC52×C7 ⋊ Dic3
SylowC52 ⋊ C7×Dic3
HallC3×C7 ⋊ #1039
SylowC3 ⋊ C7×#1039

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D5)
commutator, hypocenterC3×C52C4×C7
FrattiniC2C7×C3⋊(C5⋊D5)
Fitting, socle, prime radicalC2×C3×C52×C7C2
cosocleC2×C3×C52C2×C7
LCSG ▷ C3×C52
UCSC1 ◁ C2×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)(9,10)(11,12,13,14)(16,17)(18,19)(21,22)(23,24);(8,9,10)(20,21,23,24,22);(15,16,18,19,17)

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC49×C3⋊#1039, C72×C3⋊#1039, C7×C3⋊(C7⋊#1039), …
maximal normal subgroup ofC49×C3⋊#1039, C72×C3⋊#1039, C7×C11×C3⋊#1039, …
maximal quotient ofC49×C3⋊#1039, C72×C3⋊#1039, C7×C3⋊(C7⋊#1039), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 67);