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C25×Dic109⋊C3 #45658174

order32700
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×Dic109⋊C3
unambiguous semidirect productDic109⋊(C3×C25)
unambiguous semidirect product(C25×Dic109)⋊C3

Splittings

derived, SylowC109 ⋊ C3×C4×C25
HallC25×Dic109 ⋊ C3
HallC25×C109⋊C3 ⋊ C4
HallC25×C109 ⋊ C3×C4
HallDic109 ⋊ C3×C25
HallC109⋊C3 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25D109⋊C3
commutator, hypocenterC109C3×C4×C25
FrattiniC2×C5C5×D109⋊C3
FittingC2×C25×C109C2×C3
socle, cosocleC2×C5×C109C2×C3×C5
prime radicalC2×C5×C109⋊C3C2×C5
LCSG ▷ C109
UCSC1 ◁ C2×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 10);