Finite Group Databasebeta

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C5×C11×Dic115 #38760732

order25300
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic115

Splittings

derivedC5×C23 ⋊ C4×C5×C11
HallC52×C11×C23 ⋊ C4
HallC52×C23 ⋊ C4×C11
HallC52×C11 ⋊ Dic23
HallC11×C23 ⋊ C5×Dic5
SylowC52 ⋊ C11×Dic23
SylowC23 ⋊ C5×C11×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D115
commutator, hypocenterC5×C23C4×C5×C11
FrattiniC2C5×C11×D115
Fitting, socle, prime radicalC2×C52×C11×C23C2
cosocleC2×C5×C23C2×C5×C11
LCSG ▷ C5×C23
UCSC1 ◁ C2×C5×C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5060

Conjugacy classes & character table

6490 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25300, 69);