Finite Group Databasebeta

← Prev (#37528212) Next (#37528214) →

C7×C3⋊(Dic11⋊C25) #37528213

order23100
automorphism?
homologyAbelianization (H1) = C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(Dic11⋊C25)
unambiguous semidirect productC3⋊(C7×Dic11⋊C25)
unambiguous semidirect productDic33⋊(C7×C25)
unambiguous semidirect product(C11⋊C25)⋊(C7×Dic3)
unambiguous semidirect product(C7×Dic33)⋊C25

Splittings

derived, HallC3×C11 ⋊ C4×C7×C25
HallC3×C7×C11⋊C25 ⋊ C4
HallC7×C11⋊C25 ⋊ Dic3
HallC7×Dic33 ⋊ C25
HallC3×C11⋊C25 ⋊ C4×C7
HallC11⋊C25 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ C4×C25
HallDic33 ⋊ C7×C25
HallC7×C11 ⋊ Dic3×C25
HallC3×C7 ⋊ Dic11⋊C25
SylowC11 ⋊ C7×Dic3×C25
SylowC3 ⋊ C7×Dic11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C7×C25
FrattiniC2×C5C7×C3⋊AGL(1,𝔽11)
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C3×C5×C11C2×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 24);