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Dic21×C11⋊C25 #37528214

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

Aliases

direct productDic21×C11⋊C25
unambiguous semidirect productC3⋊(Dic7×C11⋊C25)
unambiguous semidirect productC7⋊(Dic3×C11⋊C25)
unambiguous semidirect product(C11×Dic21)⋊C25

Splittings

derived, HallC3×C7×C11 ⋊ C4×C25
HallC3×C7×C11⋊C25 ⋊ C4
HallC7×C11⋊C25 ⋊ Dic3
HallC11×Dic21 ⋊ C25
HallC3×C11⋊C25 ⋊ Dic7
HallC7×C11 ⋊ Dic3×C25
HallC3×C11 ⋊ C25×Dic7
HallC3×C7 ⋊ C4×C11⋊C25
SylowC11 ⋊ C25×Dic21
SylowC7 ⋊ Dic3×C11⋊C25
SylowC3 ⋊ Dic7×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC2×C5D21×C11⋊C5
commutator, hypocenterC3×C7×C11C4×C25
Fitting, socle, prime radical, cosocleC2×C3×C5×C7×C11C2×C5
LCSG ▷ C3×C7×C11
UCSC1 ◁ C2×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 25);