Finite Group Databasebeta

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C5×(C103⋊C3)⋊Dic5 #44525437

order30900
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×(C103⋊C3)⋊Dic5
unambiguous semidirect product(C103⋊C3)⋊(C5×Dic5)
unambiguous semidirect productDic515⋊(C3×C5)
unambiguous semidirect product(C5×Dic515)⋊C3

Splittings

derivedC5×C103 ⋊ C3×C4×C5
HallC5×Dic515 ⋊ C3
HallC52×C103⋊C3 ⋊ C4
HallC52×C103 ⋊ C3×C4
HallC103⋊C3 ⋊ C5×Dic5
SylowC103 ⋊ C3×C5×Dic5
SylowC52 ⋊ (C103⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C5C5⋊(D103⋊C3)
commutator, hypocenterC5×C103C3×C4×C5
FrattiniC2C5×C5⋊(D103⋊C3)
Fitting, socleC2×C52×C103C2×C3
prime radicalC2×C52×C103⋊C3C2
cosocleC2×C5×C103C2×C3×C5
LCSG ▷ C5×C103
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2060

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30900, 43);