Finite Group Databasebeta

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C25×(C103⋊C3)⋊C4 #44525404

order30900
automorphism?
homologyAbelianization (H1) = C3×C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×(C103⋊C3)⋊C4
unambiguous semidirect product(C103⋊C3)⋊(C4×C25)
unambiguous semidirect productDic103⋊(C3×C25)
unambiguous semidirect product(C25×Dic103)⋊C3

Splittings

derived, SylowC103 ⋊ C3×C4×C25
HallC25×Dic103 ⋊ C3
HallC25×C103⋊C3 ⋊ C4
HallC25×C103 ⋊ C3×C4
HallDic103 ⋊ C3×C25
HallC103⋊C3 ⋊ C4×C25

Subgroups

subgroupG/H
center, hypercenterC2×C25D103⋊C3
commutator, hypocenterC103C3×C4×C25
FrattiniC2×C5C5×D103⋊C3
FittingC2×C25×C103C2×C3
socle, cosocleC2×C5×C103C2×C3×C5
prime radicalC2×C5×C103⋊C3C2×C5
LCSG ▷ C103
UCSC1 ◁ C2×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10300

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 10);