Finite Group Databasebeta

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C11×C25×Dic23 #38760667

order25300
automorphism?
homologyAbelianization (H1) = C4×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×Dic23

Splittings

derived, SylowC23 ⋊ C4×C11×C25
HallC11×C23×C25 ⋊ C4
HallC23×C25 ⋊ C4×C11
HallC11×C23 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C11×C25D23
commutator, hypocenterC23C4×C11×C25
FrattiniC2×C5C5×C11×D23
FittingC2×C11×C23×C25C2
socle, prime radicalC2×C5×C11×C23C2×C5
cosocleC2×C5×C23C2×C5×C11
LCSG ▷ C23
UCSC1 ◁ C2×C11×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25300

Conjugacy classes & character table

7150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 4);