Finite Group Databasebeta

#44476186

order30304
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC947 ⋊ #108

Subgroups

subgroupG/H
centerC4D3788
commutatorC4×C947C2×C4
FrattiniC2×C4C2×D947
FittingC2×C8×C947C2
socleC2×C947C4⋊C4
prime radicalC22×C947Q8
cosocleC2×C4×C947C22
hypercenterC2×C8D947
hypocenterC947#108
LCSG ▷ C4×C947 ▷ C2×C947 ▷ C947
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15152

Polycyclic presentation:

2^5,947|a^2=d,b^2=c,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^946

Conjugacy classes & character table

7582 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30304, 82);