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C11×C25×Dic17 #34035121

order18700
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×Dic17

Splittings

derived, SylowC17 ⋊ C4×C11×C25
HallC11×C17×C25 ⋊ C4
HallC17×C25 ⋊ C4×C11
HallC11×C17 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D17
commutator, hypocenterC17C4×C11×C25
FrattiniC2×C5C5×C11×D17
FittingC2×C11×C17×C25C2
socle, prime radicalC2×C5×C11×C17C2×C5
cosocleC2×C5×C17C2×C5×C11
LCSG ▷ C17
UCSC1 ◁ C2×C11×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18700

Conjugacy classes & character table

5500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18700, 6);